Question: Instruction: Answer the following items. Show necessary solutions clearly. 1. Find the number of positive divisors of 1000 in between 500 to 1000. 2. Let

Instruction: Answer the following items. Show necessary solutions clearly.

1. Find the number of positive divisors of 1000 in between 500 to 1000.

2. Let X = {1,2...... 100} and let S = {(a,b)la.bX,a+b=50}. Find |S|.

3. Let E= {a,b,c,...,x,y,z) be the set of 26 English alphabet. How many 5 letter word can we form from E such that no vowels are together? the letters j and c are always together?

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